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Modeling Acoustic Backscatter: Gradual or Punctuated Evolution?
John Horne
FHL 2008
LO: Evaluate basis and assumptions underlying historical and current acoustic backscatter models for fish and zooplankton.
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What is a ‘Model’?
Parsimonious representation of the truth
If life was simple:
rigid body – 1 wave equation, analytic solution for 11 shapes
But
Elastic – 3 coupled scale equations, solution limited to 3 shapes: sphere, infinite cylinder, infinite rectangular slab
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Model Categories & Analytic Methods
Organism or Structure:
Zooplankton, Fish, Body, Fish Swimbladder, Whole Fish
Rayleigh
Resonance
Geometric
Exact
Nummeric
Empirical
Statistical
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Imaging Evolution
“… models based on simple geometric shapes, …, are inadequate, if only because such shapes are symmetrical with respect to the horizontal or transverse plane, while the general swimbladder is not.” (Foote 1985)
Walleye Pollock (Gadus chalcogrammus)
“…fish and zooplankton should be described by simple theories and models, without acoustically-superfluous extensions.” (Medwin and Clay 1998)
Walleye Pollock
CAT scans:
head to tail
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Limitation of Geometric Forms
“… models based on simple geometric shapes, …, are inadequate, if only because such shapes are symmetrical with respect to the horizontal or transverse plane, while the general swimbladder is not.”
“The consequence of asymmetry in swimbladder form is often observed in the significant asymmetry of dorsal and ventral aspect target strength functions of the same fish.”
Foote 1985
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Geometric Form Exception
geometric shapes are viable representations when modeling resonant or Rayleigh scattering
Why?
orientation doesn’t matter, targets are point scatterers
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Affect of Image Resolution What level of detail is acoustically appropriate?
Jech and Horne 1998
KRM Model Predictions
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Backscatter Model Alphabet Soup BEM - Boundary Element Method
DCM - Deformed Cylinder Model
DWBA - Distorted Wave Born Approximation
PT-DWBA - Phase-tracking DWBA
SDWBA – Stochastic DWBA
FEM - Finite Element Method
FMM - Fourier Matching Method
KA - Kirchhoff Approximation
KRM - Kirchhoff-ray Mode
MSS - Modal Series Solution
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Model Evolution
Geometric Anatomical
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Boundary Element Method
Calculated using Hemholtz intergral for amplitude and displacement from any point on discretized surface (where l<1/3λ)
Capabilities: valid at all frequencies, accuracy depends on quality of discretization, includes diffraction
Limitations: computationally intensive
-2
0
2
-5
0
5
-2
0
2
x (cm)y (cm)
z (c
m)
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Deformed Cylinder Model
Exact modal series solution for infinite cylinder (used for prolate spheroid swimbladder)
Capabilities: variety of material properties
Limitations: restricted angle range, arbitrary shape
x
asb(x) k = ω / c cosθ
θ
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Distorted Wave Born Approximation Designed for weak scattering objects, density differences, can integrate pieces to accommodate phase differences Capabilities: valid for all frequencies, at all angles, for any arbitrarily shaped object with small contrast in sound speed and density (body) Limitations: weakly scattering objects (g, h near unity), inhomogenous mediums
ki
ρ1, c1
ρ2, c2
ρ3, c3
dx
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Fourier Mode Matching Exact anatomical representation, exact solution for finite-length objects Capabilities:, all frequencies, all orientation angles, all scattering geometries (back, forward, and bistatic), all boundary conditions Limitations: far-field scattering, axisymmetric shape, numerical implementation, frequency and/or shape irregularity, conformal mapping (single-valued radius and “needle points”)
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Kirchhoff Approximation Surface backscatter using Kirchhoff integral
Capabilities: valid for geometric frequencies, for any shape, high or low resolution morphometry
Limitations: typically applied to swimbladder only, restricted angle range
-2
0
2
-5
0
5
-2
0
2
x (cm)y (cm)
z (cm
)
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Kirchhoff-ray Mode Breathing mode at or below resonance (ka <0.15), surface backscatter using Kirchhoff integral, cylindrical anatomical representation
Capabilities: any shape, unlimited inclusions, backscatter from all interfaces
Limitations: forced symmetry, restricted angle range, no diffraction
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Prolate Spheroidal Mode Scalar wave equation, spheroidal coordinates, spheroidal wave function (angle, radial function)
X axis
Dorsal View
Capabilities: theoretically valid for all frequencies, at all angles
Limitations: geometric representation, strong scattering objects (?)
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Finite difference, time domain
G. Macaulay
plane wave, c=1491 m/s,
τ = 0.32 ms, f = 38 kHz
Black oreo (Allocyttus niger)
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Summary Model Comparison
Model
Organism Representation
Analytic Method
BEM Anatomical, triangular mesh Hemholtz equation
Conformal Mapping
anatomical shape Hemholtz equation
DWBA deformed anatomical cylinders
line integral
KRM anatomical cylinders breathing mode + Kirchhoff
Finite Difference
actual shape, density finite difference, time domain
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Backscatter Model Comparisons
McClatchie et al. 1996
Blue Whiting (Micromesistius australis)
37 cm
29 cm
Tilt averaged
5o, 15o
mapping, deformed cylinder, equicylinder
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Expanded Model Comparisons
Fourier Matching Method (FMM) (aka Conformal Mapping) vs Anderson sphere, deformed cylinder, t-matrix, BEM, exact prolate spheroid, Kirchhoff approximation
Swimbladder cross-section
Reeder & Stanton 2004
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Model Comparison to Empirical Measures Finite Boundary Element (BEM) Model and Kirchhoff approximation
Pollack (Pollachius pollachius)
Tilt angle (deg) Tilt angle (deg)
38 kHz 120 kHz
Foote and Francis 2002
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Workshop: Herring Results
Length Frequency
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Workshop: Herring Results
38 kHz
Lateral
38 kHz
Dorsal-Ventral
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Comparing Models to Finite Solutions Model Comparison to
Prolate Spheroid Model Comparison to Jack
Mackerel Swimbladder
PSMS: Prolate Spheriod Modal Series; KA: Kirchhoff Approximation; KRM: Kirchhoff Ray Mode; FE: Finite Element
Macaulay et al. 2013
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Backscatter Modeling Conclusions
- Organism representations evolved from geometric shapes to anatomical detail, exact to numeric solutions
- Image resolution continues to increase, no standard
- Validation by comparison to exact solutions, other models, empirical measures
- Gradual evolution with punctuations
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Kirchhoff-Ray Mode Model
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Length (mm)100 200 300 400 500
Targ
et S
treng
th (d
B)
-55
-50
-45
-40
-35
-30
120 kHz90 degrees
KRM Backscatter Predictions
Frequency (kHz)0 100 200 300 400
Targ
et S
treng
th (d
B)
-55
-50
-45
-40
-35
-30
150 mm90 degrees
Tilt Angle (degrees)70 80 90 100 110
Targ
et S
treng
th (d
B)
-55
-50
-45
-40
-35
-30
120 kHz200 mm
Length
Frequency
Tilt
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Backscatter Response Surface: Walleye Pollock
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KRM Backscatter Ambit
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Validation of Kirchhoff-Ray Mode Model
Comparison to Nakken and Olsen (1977) Atlantic cod (Gadus morhua) maximum target strength measurements at 38 kHz
Comparison to Jech et al. (1995) Threadfin shad (Dorosoma petenense) target strength measurements at 120, 200, and 420 kHz.
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Comparing Models to Empirical Measures
60 80 100 120 140 160
Targ
et S
treng
th (d
B)
-54
-52
-50
-48
-46
-44
-42
-40
-38
Length (mm) Caudal Length (mm)400 600 800 1000 1200
Targ
et S
treng
th (d
B)
-70
-60
-50
-40
-30
-20
-70
-60
-50
-40
-30
-20
Lavnun 120 kHz Paddlefish 200 kHz
Horne et al. 2000 Hale et al. 2003
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Comparing Models to Empirical Measures
Walleye pollock
100 200 300 400 500 600
Targ
et S
treng
th (d
B)
-55
-50
-45
-40
-35
-30
-25
TS=20log(L)-66
Fork Length (mm)100 200 300 400 500 600
Targ
et S
treng
th (d
B)
-60
-55
-50
-45
-40
-35
-30
-25
(b) 120 kHz
(a) 38 kHz
38 kHz
120 kHz
Horne 2003
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Fish Ensemble Visualization
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Fish-Cam Visualization
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Acoustic Fish Behavior Simulator
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Model Applications: TS - length
Length (mm)100 200 300 400 500 600
Targ
et S
treng
th (d
B)
-50
-45
-40
-35
-30
-25
TS=20log(L)-66
38 kHz n= 48 fish
Horne 2003
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Acoustic Backscatter Characterization
eulachon
(Thaleichthys pacificus)
capelin
(Mallotus villosus)
Pacific herring
(Clupea pallasii)
walleye pollock (Theragra
chalcogramma)
Atka mackerel (Pleurogrammus monopterygius)
Gauthier & Horne 2004a
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Acoustic Species Discrimination
capelin
Pacific herring
walleye pollock
Atka mackerel
eulachon
Gauthier & Horne 2004b
200-12 kHz
120-38 kHz
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Aquatic Organism Distributions
Aggregation types: individuals; small pure groups; mixed resolvable groups; unresolvable groups
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Estimating Population Abundance
Jech & Horne 2001
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Walleye Pollock Tilt Distributions: 8 m3 Laboratory Tank
Tilt (degrees)0 20 40 60 80 100 120 140 160 180
Freq
uenc
y
0
25
50
75
200
n=932density p=0.17time p=0.89
head up head down
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W Pollock Length & Target Strengths
Walleye Pollock Lengths
Length (cm)
25 30 35 40 45 50 55
Freq
uenc
y
0
10
20
30
40
50
60
25 30 35 40 45 50 550
10
20
30
40
50
60
Target Strength (dB)-60 -50 -40 -30 -20
Freq
uenc
y
0
50
100
150
200
250
300
Walleye Pollock Target Strength
-60 -50 -40 -30 -20
Freq
uenc
y
0
50
100
150
200
250
300
Freq
uenc
y
haul 77n=427
haul 78n=364
38 kHz
120 kHz
Bering Sea, July 2000
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Simulating TS Distributions
-60 -50 -40 -30 -20
Freq
uenc
y
0
50
100
150
200
250
300
-70 -60 -50 -40 -30 -20
Freq
uenc
y
0
10
20
30
40
50
-70 -60 -50 -40 -30 -20
Freq
uenc
y
0
10
20
30
40
50
60
70
-70 -60 -50 -40 -30 -20
Freq
uenc
y
0
5
10
15
20
25
30
35
Target Strength (dB)
-60 -50 -40 -30 -20
Freq
uenc
y
0
50
100
150
200
250
300
-70 -60 -50 -40 -30 -20
Freq
uenc
y
0
10
20
30
40
50
-70 -60 -50 -40 -30 -20
Freq
uenc
y
0
10
20
30
40
50
-70 -60 -50 -40 -30 -20
Freq
uenc
y
0
10
20
30
40
50
Target Strength (dB)
In situ 38 kHz
leng-freq+tilt-freq+KRM
In situ 120 kHz
leng-freq+tilt-freq+KRM
leng-freq+tilt-freq+KRM leng-freq+tilt-freq+KRM
leng-freq+tilt-freq+KRM leng-freq+tilt-freq+KRM
38 kHz 120 kHz
Length + Tilt +
KRM
In situ